In lithography by an electron beam, it has been known to use a variable shaping type electron beam lithography apparatus, in which a sectional shape of the electron beam is shaped into a rectangular shape by passing a mask having a rectangular opening. Hereinafter, discussion will be given in terms of the variable shape type electron beam lithography apparatus.
When a plotting pattern is formed by irradiating the electron beam on a photosensitive material (hereinafter referred to as resist) on a substrate of a semiconductor wafer, exposure mask, reticle and so forth, and by chemical reaction of the resist, in addition to a primary exposure by incident electron with small scattering radius and having high resolution, there is another exposure caused by penetration of a part of the irradiated electron beam through the resist into the substrate, becoming large scatter with large scattering radius in the substrate to re-incident into the resist layer. There are two classes of irradiated electron scattering. Exposure caused by incident electron is called forward scattering. The latter having large scattering radius is called backward scattering. In a region occupied wide area by the plotting pattern, namely a region having a high exposure area ratio, excessive exposure condition can be caused by influence of backward scattering in the adjacent region to cause deformation of the plotting pattern, such as collapsing of pattern or the like. This phenomenon is generally caused by intrinsic deflection. For the measure of the intrinsic deflection, various methods for correcting exposure energy have been proposed.
One example of a correction method is to preliminarily calculate deformation due to intrinsic deflection of the plotting pattern and to preliminarily add a deformation amount compensating the deformation to data expressing the plotting pattern. A predictive calculation method of the deformation amount is complicated and not practical.
The second example is to perform lithography by adjusting the exposure energy upon plotting by canceling the exposure effect by backward scattering. This method is an exposure energy correction with taking a value defined as the exposure area ratio relative to a unit area of the plotting as indicia. When the backward scattering radius is significantly larger than the plotting pattern, influence of the backward scattering becomes substantially uniform and can be regarded to be proportional to the exposure area ratio. Consideration of adjusting exposure energy by varying the exposure period depending upon the exposure area ratio has been proposed, and has been disclosed in Japanese Patent Publication No. 58-32420, Japanese Patent Publication No. 59-139625, Japanese Patent Publication No. 61-284921 and Japanese Patent Application Laid-Open No. 10-229047, for example.
On the other hand, a method for determining the exposure energy in consideration of a dimension of the plotting pattern for enhancing effect of correction has been disclosed in Japanese Patent Application Laid-Open No. 10-189422. Also, a method for determining an auxiliary exposure pattern in consideration of the exposure area ratio and the distance of the peripheral portion of the region exposed at one time to add the exposure energy has been disclosed in Japanese Patent Application Laid-Open No. 11-111595.
Concerning exposure energy correcting method disclosed in the foregoing Japanese Patent Application Laid-Open No. 229047, discussion will be given with reference to FIG. 2. FIG. 2 is a block diagram showing a construction of a control circuit for correction of intrinsic deflection in the variable shape type electron beam lithographic apparatus.
In an auxiliary storage device (not shown) provided in the control unit 4, data of the plotting pattern is stored. Data of the plotting pattern is initially restored into independent basic pattern data by a restoring circuit (not shown) for data. Then, in a pattern decomposition circuit (not shown), the basic pattern data is decomposed into an aggregate of rectangular area pattern data smaller than a dimension of the region to be exposed during a single irradiation of the electron beam. Here, the plotting region on the substrate is defined into separate regions, each of which can be exposed by a single irradiation of the electron beam. The separated regions will be hereinafter referred to as partial regions.
Outputs from the pattern decomposition circuit are a signal indicative of an electron beam irradiation period per the partial region on the substrate, a signal indicative of longitudinal and lateral dimensions of the rectangular pattern, and a signal indicative of the position coordinates.
An irradiation period T of the electron beam, longitudinal and lateral dimensions (H, W) of the rectangular pattern, position coordinates (X, Y) of the rectangular pattern from the pattern decomposition circuit are shown in FIG. 2.
When correction for intrinsic deflection is not performed or when calculation of correction for intrinsic deflection is preliminarily performed, the irradiation period T is directly input to a blanking control circuit 1 without passing through an intrinsic deflection correcting circuit 22 to be converted into radiation/non-radiation timing signal of the electron beam.
The longitudinal and lateral dimensions (H, W) of the rectangular pattern are input to a dimension control circuit 3 and then converted into an analog signal for forming an electron beam section and input to an electron beam plotting device. The position coordinates (XC, Y) of the rectangular pattern is input to a deflection control circuit 5 to be converted into an analog signal for position deflection and then input to the electron beam plotting device.
Upon performing correction of intrinsic deflection with taking the exposure area ratio as indicia, within the radiation period T, a real time correction, in which exposure, exposure energy calculation, correcting exposure energy calculation are repeated sequentially, is executed. Then, a new irradiation period is input to the blanking control circuit 1. For correction of the irradiation period T to be performed by the intrinsic deflection correcting circuit 22, an exposure area ratio signal R per partial region calculated in an exposure area ratio calculating circuit 23 and a backward scattering coefficient ζ common to all regions are used.
Since the exposure area ratio signal R has a value varying per the partial region, they are preliminarily stored in a memory (not shown) in a form of table, in the exposure area ratio calculating circuit 23. The table is generated upon inputting the longitudinal and lateral dimensions (W, H) and position coordinates (X, Y) of the rectangular pattern.
By cumulatively adding W×H per each region with taking upper bit of the memory (not shown) storing the position coordinates (X, Y) as table coordinates, the table of the exposure area ratio can be easily generated. Subsequently, the numerical value of each region is smoothed by averaging with other numeral values of other regions of the range where the backward scattering influences to take the numeral value after smoothing as numerical value of the partial area, or other methods. The smoothing process is a setting processing of the backward scattering diameter â, and weighting in smoothing or number of times of repetition are selected depending upon the backward scattering diameter â to be set.
The exposure area ratio calculating circuit 23 performs a linear interpolation of the exposure area ratio R by position coordinates (X, Y) upon plotting, to output an interpolation value to the intrinsic deflection correcting circuit 22.
Correction calculation to be performed by the intrinsic deflection correction circuit 22 is performed in the following manner. Among the exposure energy, the energy by forward scattering will be hereinafter referred to as a plotting portion supposed forward scattering accumulated energy. Then, the amount of the plotting portion supposed forward scattering accumulation energy is assumed as one. Contribution of the forward scattering upon plotting of the plotting pattern is defined to be half of the plotting portion supposed forward scattering accumulation energy at the plotting edge.
The reason is discussed here below. A longitudinal section of the plotting pattern is considered. The exposure energy necessary for plotting the plotting pattern is assumed to be one and the exposure energy of the region around the plotting pattern is assumed to be zero, the rectangular exposure energy of 0, 1, 0 in horizontal direction in design. However, actually, in the edge portion of the plotting pattern, so-called blurring is caused. Therefore, it is not possible to abruptly vary the energy of the electron beam from zero to one and from one to zero. The beam takes a trapezoidal form having a gradient between zero and one. Accordingly, in a region of horizontal direction of the level of the energy in design, the peak portion of the wave becomes smaller and a region at the bottom of the wave, where the energy is zero, becomes larger. Upon defining the dimension in the horizontal direction of the plotting pattern of the rectangular pattern in design, dimensions are different between the peak and the bottom of the wave, in a trapezoidal manner, as set forth above. The tilted portion of the trapezoidal shape and the rectangular shape intersect at a point of ½ height. Therefore, the dimension in the horizontal direction is defined at the point of the ½ height of the trapezoidal shape, namely at the point where the energy becomes ½. With this, even when the gradient of the trapezoidal shape indicative of the exposure energy is varied, the position of the point where the height is ½, where the titled portion of the trapezoidal shape and the rectangular shape intersect, in the horizontal direction is not varied. Accordingly, by defining the actually drawn dimension, the dimension can be matched with the designed dimension of the rectangular shape.
Taking an optimal exposure period t50 in a line and space pattern of 1:1, where the line width and line interval of the plotting pattern are the same and the exposure area ratio becomes 50%, as reference, the exposure period t can be expressed by the following equation relative to the exposure area ratio R.t(R)=t50·(1+η)/(1+2·η·R)  (1)
The form of the foregoing expression (1) is to match the accumulated energy of the edge portion of the plotting pattern as set forth above, and to match the designed dimension and the plotting dimension. The reason why the reference of the optimal exposure period is taken as 1:1 line and space pattern where the exposure area ratio is 50%, is that the accumulated energy of the electron beam at the edge potion of the plotting pattern with respect to scattering of all scattering diameter in this condition constantly becomes ½ of the plotting portion supposed accumulated energy, and the plotting dimension dependency of the optimal exposure period is not present. To understand this, consider a condition where the plotting pattern is returned at the plotting edge. In this condition, across the plotting edge, one side is an entirely drawn area and the other side is a non-drawn area. However, the accumulated energy of the plotting edge portion of the 1:1 line and space pattern where the exposure area ratio is 50%, is equivalent to the edge portion of the one side entirely drawn area. Therefore, it does not depend on the plotting line width or the scattering diameter.
An electron beam scattering parameter to be used for correction of intrinsic deflection, using the foregoing exposure area ratio as indicia, is only two kinds of a backward scattering coefficient ζ as backward scattering integrated intensity versus forward scattering integrated intensity and a backward scattering diameter β. The integrated intensity of the forward scattering is only dealt as a reference of the integrated intensity of the backward scattering. The reason is that, for example, in the case that the accelerating voltage of the electron is about 50 kV, the scattering diameter of the backward scattering is about 10 μm, whereas the scattering diameter of the forward scattering is about 50 nm which is as small as less than or equal to 1/100 of the former.
Taking the forward scattering as a simple reference, in case of correction method for correcting only influence of the backward scattering, with respect to a plotting pattern having a line width greater than or equal to 300 nm, relatively better correction result can be obtained. However, in case of the plotting pattern having line width less than or equal to 200 nm, in a region where the exposure area ratio is small, it becomes apparent that insufficient exposure energy can be caused at smaller line width of the plotting pattern. The reason is that an intermediate scattering having scattering diameter in the extent of 300 nm which has not be considered conventionally, cannot be ignored. In order to more accurately describe electron scattering, intermediate scattering having scattering diameter in the extent of 300 nm in description of three Gaussian distribution has to be considered.
Furthermore, when a highly sensitive chemical amplification type resist is used on the substrate, the influence becomes significant. Sensitivity of the chemical amplification type resist depends on the scattering width of acid catalyst dominant for chemical reaction and generated by irradiation of the electron beam relative to essential forward scattering, since it appears to cause expansion of the forward scattering diameter. For example, a condition to obtain ten times higher sensitivity in the chemical amplification type resist, is a condition to scatter the acid catalyst over a region of ten times in area ratio with respect to the essential forward scattering region. Since the intermediate scattering diameter is close to the forward scattering diameter and significantly different from the backward scattering diameter, it can be approximated by the forward scattering diameter. However, it has been known that the apparent forward scattering diameter at this time is expanded up to about 200 nm which is four times the conventionally supposed forward scattering diameter of 50 nm.
A reason why expansion of the effective forward scattering diameter is a problem will be discussed in terms of plotting an isolated line having a large aspect ratio and relatively distant from other plotting pattern, with reference to FIG. 3. FIG. 3 is a graph showing distribution of accumulated energy in line width direction by forward scattering upon plotting of the isolated line, (a) is the case where the plotting line width is taken as parameter, (b) shows a comparison of ideal distribution and actual distribution of the forward scattering accumulated energy ratios when the plotting line width is double the forward scattering diameter, and (c) shows a comparison of ideal distribution and actual distribution of the forward scattering accumulated energy ratios when the plotting line width is equal to the forward scattering diameter. Here, a position x/α is a position in a unit standardization with the effective forward scattering diameter α and the value of plotting edge is assumed as 0. On the other hand, the forward scattering accumulated energy ratio is a ratio of forward scattering accumulated energy at the position x/α and supposed accumulated energy of the plotting portion.
In FIG. 3(a), when the line width w of the plotting pattern is greater than double the effective forward scattering diameter α, for example, when line width w/α=4.0, as shown by an asterisk mark *, the accumulated energy ratio at the supposed plotting edge of the position x/α=0 constantly becomes half of the supposed accumulated energy of the plotting portion at the position of x/α=2. In contrast to this, when the line width of the plotting pattern becomes smaller in relation to the effective forward scattering diameter α, the electron beam accumulated energy at the plotting edge is lowered to be smaller than half of the supposed accumulated energy of the plotting portion at the position of x/α=2, and the accumulated energy at the center of the line width of the plotting pattern is also lowered. This condition will be discussed with reference to FIGS. 3(b) and 3(c).
When the line width w of the plotting pattern is double the effective forward scattering diameter α, in FIG. 3(b), a distribution of the accumulated energy by forward scattering electron, shown by the white diamond shape of sign , becomes smaller than the ideal wave shape distribution, shown by the white square of sign □. However, the forward scattering accumulated energy ratio at the supposed plotting edge at the position x/α=0 and the electron beam accumulated energy at the supposed plotting edge is half of the plotting portion supposed accumulated energy, the line width by the distribution of the accumulated energy and the line width in design are matched. Accordingly, in plotting of this pattern, supposed line width can be obtained without correction as shown by black square of sign ▪.
On the other hand, when the plotting line width w is equal to the effective forward scattering diameter α, in FIG. 3(c), the position where the plotting portion supposed accumulated energy becomes half becomes inside of line width than the supposed plotting edge at the position of x/α=0 and the electron beam accumulated energy does not make plotting impossible. When plotting is performed without correction, insufficient exposure energy makes the line thinner than the line width w/α=1.
Furthermore, when the plotting line width is thin, as shown by black diamond of sign ♦ of FIG. 3(a), the region where the plotting portion supposed accumulated energy is half is not present to make it impossible to perform plotting per se.
This condition is shown aggregatingly in FIG. 4. FIG. 4 is a graph showing plotting line width dependency of the forward scattering accumulated energy ratio showing plotting line width dependency of the accumulated energy by the forward scattering electron at the plotting center and the plotting edge portion upon plotting of the isolated line, in which a horizontal line represents a ratio versus the forward scattering diameter of the design line width. In FIG. 4, when the plotting dimension becomes smaller than double the effective forward scattering diameter, the electron beam accumulated energy of the designed edge portion of the line form plotting pattern is lowered to place the position where the forward scattering accumulated energy ratio is 0.5, namely the position where the plotting portion supposed accumulated energy becomes half, is located inside of the plotting line width to cause thinning of the line width with respect to the design dimension of the line width. Furthermore, when the plotting dimension is about equal to the effective forward scattering diameter, the peak value of the electron beam accumulated energy also becomes less than or equal to half of the plotting portion supposed accumulated energy to make image formation per se impossible. These conditions are exemplified in plotting of w/α=1.0 and w/α=0.5 in FIG. 3.
Therefore, upon fine dimension plotting, it becomes necessary to perform exposure energy adjustment depending upon plotting dimension. Desired correction is the correction to make the forward scattering accumulated energy ratio of the edge portion of the isolated line 0.5 without depending upon the plotting dimension as shown in FIG. 9.
Exposure energy adjustment depending upon the plotting dimension as set forth above has been discussed in Japanese Patent Application Laid-Open No. Heisei 10-189422. By performing correction as set forth above, the distribution of the forward scattering accumulated energy ratio corresponding to FIG. 3(a) is as shown in FIG. 5(a). In comparison with FIG. 3(a), the accumulated energy ratio is increased.
FIG. 5(b) shows distribution of the forward scattering accumulated energy ratio upon plotting correction when the plotting line width w is equal to the effective forward scattering diameter α, similarly to FIG. 3(a) to permit plotting as supposed. On the other hand, FIG. 5(c) shows distribution of the forward accumulated scattering accumulated energy ratio upon plotting correction in the case where the plotting line width w is half of the effective forward scattering diameter α. However, even in this case, plotting as supposed can be performed.
In the prior art disclosed in Japanese Patent Application Laid-Open No. Heisei 10-189422, the need for exposure energy adjustment depending upon plotting dimension is attributed to insufficient exposure energy due to insufficient accuracy in dimension measurement. Namely, in the prior art, the same correction is applied irrespective of the exposure area ratio. In this correction, a problem is newly encountered in that over-dosing is caused in line and space pattern where the exposure area ratio is 50% or in the plotting pattern of high exposure area ratio where the interval between lines is smaller than the line width to cause collapse of the pattern.
FIGS. 6 and 7 are graphs showing the forward scattering accumulated energy distribution similarly to FIG. 3 or 5, and show the case of line and space pattern plotting. The discussion given hereinafter shows only the influence of the effective forward scattering and does not include influence of the backward scattering. However, in practice, since the accumulated energy due to backward scattering electron which can be regarded as substantially constant, is added, a wider line width than the result set forth later is drawn.
In the line and space pattern of the exposure area ratio being 50% where the ratio between the line width and the interval there between is 1:1, the value of the electron beam accumulated energy at the plotting edge before exposure energy correction constantly becomes half of the plotting portion supposed accumulated energy irrespective of the plotting dimension. In contrast to this, when correction for the isolated thin line disclosed in the prior art and the same line width dependent correction are added to this pattern, the electron beam accumulated energy is increased to cause over-dosing as shown in FIG. 7, and the plotting area shown by the black square of sign ▪ becomes wider in comparison with the case of FIG. 6 to cause thickening of the dimension.
This phenomenon is shown in FIG. 8. FIG. 8 shows over-dosing to be caused in line and space pattern where the exposure area ratio is 50% and the ratio between the line width and the interval therebetween is 1:1. FIG. 8 is a graph showing the dependency of plotting line width on the forward scattering accumulated energy ratio. The horizontal axis represents a ratio of the designed line width versus the forward scattering diameter. In FIG. 8, when the line width dependent correction required for plotting the isolated thin line is performed for the line and space pattern where the ratio between the line width and the interval therebetween is 1:1, over-dosing can be caused at higher frequency at smaller plotting pattern as shown in FIG. 8.
In the prior art set forth above, the example of plotting of the line and space pattern shown in FIGS. 6, 7 and 8 only shows influence of the effective forward scattering and does not include influence of the backward scattering. However, in practice, the accumulated energy due to backward scattering electron which can be regarded substantially constant, is added. Therefore, since resolution of the fine pattern of line and space of 1:1 is difficult from the beginning, a pattern where the line interval is wider than the drawn line width is drawn in practice. However, even in this case, when the drawn line width and the line interval become smaller, in the correction method by the foregoing prior art, pattern collapsing where thickening of the line dimension and coupling of the lines, can be caused.